Another copula family that can be
employed in high dimensions are vine copulas [1]}, [2]}.
These are constructed from bivariate copula
building blocks called “pair-copulas” by [3]}.
By selecting different pair-copulas, vines can be constructed with
a wide range of dependence structures; see [4]} for an overview.
Vines are based on a decomposition
into conditional distributions.
In some applications an appropriate decomposition
arises naturally, such as with time series as in [5]},
or when conditioning on latent factors as in [6]}, [7]}.
But, in general, there are many different possibilities [8]} and it can be difficult to select an appropriate choice,
although there have been advances in
approaches to do so [4]}. Another challenge in high dimensions is that
it can be slow to evaluate the copula density and simulate from the vine, both of which
are necessary for parameter estimation and inference.
However, truncation as in [10]}
or other simplifications, such as for stationary Markov time series [5]}, [12]}, [13]},
can alleviate these problems. In contrast, it is often unnecessary to evaluate
the implicit copula density when estimating the copula model, and simulation
from high dimensional
implicit copulas is typically fast and stable using Algorithm REF .
